which is the graph of $f(x)=x^{2}-2x + 3$?

Explanation:

Step1: Find the vertex of the parabola

For a quadratic function (y = ax^{2}+bx + c), the (x) - coordinate of the vertex is given by (x=-\frac{b}{2a}). For (f(x)=x^{2}-2x + 3), where (a = 1), (b=-2), (c = 3). (x=-\frac{-2}{2\times1}=1). Substitute (x = 1) into the function: (y=(1)^{2}-2\times(1)+3=1 - 2+3=2). So the vertex is ((1,2)).

Step2: Find the (y) - intercept

The (y) - intercept is found by setting (x = 0). When (x = 0), (y=(0)^{2}-2\times(0)+3=3). So the (y) - intercept is ((0,3)).

Answer:

The graph with vertex ((1,2)) and (y) - intercept ((0,3)) (the first graph in the image, assuming the first graph has vertex at ((1,2)) and passes through ((0,3))) is the graph of (f(x)=x^{2}-2x + 3).